We investigate the behaviour of a short cavity swept source laser with an intra cavity swept filter both experimentally and theoretically. We characterise the behaviour of the device with real-time intensity measurements using a fast digital oscilloscope, showing several distinct regimes, most notably regions of mode-hopping, frequency sliding mode-locking and chaos. A delay differential equation model is proposed that shows close agreement with the experimental results. The model is also used to determine important quantities such as the minimum and maximum sweep speeds for the mode-locking regime. It is also shown that by varying the filter width the maximum sweep speed can be increased but at a cost of increasing the instantaneous linewidth. The consequent impacts on optical coherence tomography applications are analysed.